May someone give me a hint for part (b) please?
Radiocarbon dating can be used to estimate the age of material, such as animal bones or plant remains, that comes from a formerly living organism. When the organism dies, the amount of carbon-$14$ in its remains decays exponentially. Suppose that $f(t)$ is the amount of carbon-$14$ in an organism at time $t$ (in years), where $t=0$ corresponds to the time of death of the organism. Assume that the amount of carbon-$14$ is modelled by the exponential decay function $$ f(t) = Ce^{kt}\quad (t\geqslant 0), $$ where $C$ is the initial amount of carbon-$14$ and $k$ is a constant.
The half-life (or halving period) of a radioactive substance like carbon-$14$ is the time that it takes for the amount of the substance to decrease to half of its original level
$(a)$ Given that the half-life of carbon-$14$ is $5730$ years, show that the value of the constant $k$ is $-0.000121$, correct to three significant figures.
$(b)$ Suppose that some ancient animal bones have been found where the amount of carbon-$14$ is known to have decreased to $1/5$ of the level that was present immediately after the death of the animal. How much time has elapsed since the death of this animal? Give your answer to the nearest number of whole years.
I am not using the given formula
Let the number of times C-14 under goes decaying be n,
Therefore, C(1-1/2)^n = C/5 => 1/2^n = 1/5 => n = log 2(base) 5 = 3.01
Hence, Number of years = 3.01*5730 = 13,304.6 = 13305 years (approx.)